Proof of Serban's conjecture

TL;DR

This paper proves Serban's conjecture, simplifying the Green function in the Calogero-Sutherland model and linking it to Coulomb gas correlators, supporting bosonization methods for this system.

Contribution

The paper provides a proof of Serban's conjecture, enabling a new understanding of the Green function and form factors in the Calogero-Sutherland model.

Findings

Green function expression is greatly simplified

Form factors are expressed in terms of Coulomb gas correlators

Supports the existence of a bosonization procedure

Abstract

We prove Serban's conjecture which simplifies greatly the expression of the advanced single-particle Green function in the Calogero-Sutherland model. The importance of proving this conjecture is that it reorganizes the form factor in terms of two dimensional Coulomb gaz correlators and confirms the possible existence of a bosonization procedure for this system.